[1] Ashbaugh M S. Isoperimetric and universal inequalities for eigenvalues//Davies E B, Safarov Yu, eds. Spectral Theory and Geometry. Vol 273. Edinburgh: London Math Soc Lecture Notes, 1999: 95–139
[2] Chen Z C, Qian C L. On the upper bound of eigenvalues for elliptic equations with higher orders. J Math Anal Appl, 1994, 186: 821–834
[3] Cheng Q M, Huang G Y, Wei G X. Estimates for lower order eigenvalues of a clamped plate problem. Cal Var PDE, 2010, 38: 409–416
[4] Cheng Q M, Ichikawa T, Mametsuka S. Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere. Cal Var PDE, 2009, 36: 507–523
[5] Huang G Y, Li X X, Qi X R. Estimates on the first two buckling eigenvalues on spherical domains. J Geom Physics, 2010, 60: 714–719
[6] Huang G Y, Li X X, Cao L F. Universal bounds on eigenvalues of the buckling problem on spherical domains. J of Math (PRC), 2011, 31: 840–846
[7] Huang G Y, Chen W Y. Universal bounds for eigenvlaues of Laplacian operator with any order. Acta Mathematica Scientia, 2010, 30B(3): 939–948
[8] Huang G Y, Chen W Y. Ineqalities of eigenvalues for bi-kohn Laplacian on Heisenberg group. Acta Mathematica Scientia, 2010, 30B(1): 125–131
[9] Jost J, Li-Jost X Q, Wang Q L, Xia C Y. Universal bounds for eigenvalues of the polyharmonic operator. Trans Amer Math Soc, 2011, 263: 1821–1854
[10] Jost J, Li-Jost X Q, Wang Q L, Xia C Y. Universal inequalities for eigenvalues of the buckling problem of arbitrary order. Comm PDE, 2010, 35: 1563–1589
[11] Payne L E, P´olya G, Weinberger H F. On the ratio of consecutive eigenvalues. J Math Phys, 1956, 35: 289–298
[12] Hile G N, Yeh R Z. Inequalities for eigenvalues of the biharmonic operator. Pacific J Math, 1984, 112: 115–133
[13] Cheng Q M, Yang H C. Universal bounds for eigenvalues of a buckling problem. Commun Math Phys, 2006, 262: 663–675
[14] Wang Q L, Xia C Y. Universal inequalities for eigenvalues of the buckling problem on spherical domains. Commun Math Phys, 2007, 270: 759–775
[15] Wang Q L, Xia C Y. Inequalities for eigenvalues of the clamped problem. Cal Var PDE, 2011, 40: 273–289
[16] Wang Q L, Xia C Y. Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifold. J Funct Anal, 2007, 245: 334–352 |